Вычислить интеграл (2x+3)/(4x^2+4x+5) dx
4x^2+4x+5=(4x^2+4x+1)+4=(2x+1)^2+4 Замена 2x+1=t x=(t-1)/2 dx=dt/2 2x+3=t+2 ∫(2x+3)dx/(4x^2+4x+5)=∫((t+2)*dt/2)/(t^2+4)= =(1/2)∫tdt/(t^2+4)+∫dt/(t^2+2^2)= =(1/4)ln|t^2+4|+(1/2)*arctg(t/2)+C, t=2x+1